Abstract Machine learning (ML) classification models are increasingly being used in a wide range of applications where it is important that predictions are accompanied by uncertainties, including in climate and earth observation, medical diagnosis and bioaerosol monitoring. The output of an ML classification model is a type of categorical variable known as a nominal property in the International Vocabulary of Metrology (VIM). However, concepts related to uncertainty evaluation for nominal properties are not defined in the VIM, nor is such evaluation addressed by the Guide to the Expression of Uncertainty in Measurement (GUM). In this paper we propose a metrological conceptual uncertainty evaluation framework for nominal properties. This framework is based on probability mass functions and summary statistics thereof, and it is applicable to ML classification. We also illustrate its use in the context of two applications that exemplify the issues and have significant societal impact, namely, climate and earth observation and medical diagnosis. Our framework would enable an extension of the GUM to uncertainty for nominal properties, which would make both applicable to ML classification models.

Abstract Background/Purpose: Radiopharmaceutical therapy (RPT) with alpha-emitting radionuclides, such as 225Ac, offers highly localized dose delivery due to its short particle range and high linear energy transfer (LET). However, unlike external beam radiotherapy (EBRT) and brachytherapy, which have traceable absorbed dose standards, RPT currently lacks a standardized absorbed dose measurement framework. This study aims to quantify the absorbed dose to air from a 225Ac source using an extrapolation chamber, supported by Monte Carlo (MC) simulations, to establish a robust methodology for dose validation of computational methods.
Methods: An extrapolation chamber was used to measure the absorbed dose to air from a drop casted 225Ac source, with source activity determined using a Low-Energy Germanium (LEGe) detector. High-resolution 2D imaging characterized the spatial distribution of deposited activity, enabling precise source geometry modeling for MC simulations. Self-attenuation effects were quantified using alpha spectrometry, and automated voltage control improved measurement repeatability of the extrapolation chamber. Absorbed dose calculations were compared between experimental and MC results across multiple air gaps.
Results: Experimental and simulated absorbed dose values were in strong agreement, with experimental measurements consistently 1–2% higher than MC predictions across all air gaps. The ionizing-radiation Quantum Imaging Detector (iQID) system provided activity mapping for source characterization, reducing uncertainties in MC modeling. The integration of automated chamber voltage control enhanced measurement precision, while uncertainty analyses highlighted activity determination and alignment as key contributors to variability.
Conclusions: This study establishes a validated methodology for quantifying 225Ac absorbed dose using extrapolation chamber measurements. The findings support the development of traceable absorbed dose standards for RPT and highlight the need for further refinement in alignment protocols and activity quantification. Future work should explore comparisons with time-integrated activity (TIA)-based absorbed dose calculations to align experimental methodologies with clinical RPT dosimetry practices.

Abstract The realisation of the kilogram at PTB is based on the established X-ray crystal density method (XRCD). This method is based on a high-precision characterisation of spheres of isotope-enriched 28 Si. The crystal and material parameters are considered constant and do not need to be re-determined when the realisation of the kilogram is updated. Therefore, the re-determination is primarily based on new measurements of the volume and the mass of the surface layers of the 28 Si spheres.
This paper presents new insights in the XRF analysis method used in the XRCD method by PTB and its effects on the volume and mass of 28 Si spheres used as primary mass standards, which provides a basis for participation in the key comparison CCM.M-K8.2024.
In the key comparisons CCM.M-K8 from 2019, 2021 and 2024, the definition of the kilogram was realised using the AVO28-S8c and Si28kg01a spheres, as outlined in this document. When applying the new model for the spectral components of the XRF spectrum, realisation results of both spheres show an average mass increase of 13.5 µg.

Abstract We performed lattice comparison measurements between 28Si-enriched crystals using a self-referenced lattice comparator (SRLC). The relative lattice spacing difference between two crystals sectioned from the same ingot were measured, showing agreement with values calculated from impurity and vacancy corrections, as well as with those obtained by other measurement techniques. Further comparison involving crystals from different ingots enabled an independent determination of the {220} lattice-plane spacing of a 28Si enriched crystal as 192.014 712 91(55) nm, confirming previously reported values. When applied to the realization of the kilogram via the X-ray crystal density (XRCD) method, the uncertainty contribution from the SRLC measurement corresponds to 8.4 g uncertainty in the mass of a 1-kg silicon sphere, supporting its role in the accurate realization of the kilogram.

Abstract The effect of wavefront aberrations, arising from both Raman beam phase distribution and atomic cloud thermal expansion, represents a critical error in atom gravimeters. This work introduces a strategy to reduce and evaluate the effect of wavefront aberrations in an atom gravimeter. First, the optical elements were installed inside the vacuum chamber to minimize the uncertainty of wavefront aberrations effect; Second, a method based on combining precise optical surface measurements with atomic cloud parameters characterization was employed to evaluate this effect; Finally, two distinct modulation experiments were conducted to verify the correctness of the evaluation results. Based on this strategy, the uncertainty of wavefront aberrations effect was determined to be 1.4 μGal (1 μGal=1×10^-8 m/s^2), and the total uncertainty of the atom gravimeter was thus reduced to 1.6 μGal. This study proposes a comprehensive methodology for evaluating wavefront aberrations effect in atom gravimeters, which will significantly advance the development of atom interferometers toward higher precision measurements.

Abstract The National Research Council of Canada (NRC) recently piloted the second international key comparison of triple point of water cells, CCT-K7.2021, where participants submitted a transfer cell and a report of the temperature difference between their transfer cell and their respective national reference. By comparing the differences between each transfer cell, NRC could calculate the differences between each participant’s national reference. While there was good agreement among all the participants, there was a large variation among the submitted uncertainties. This was possibly due to the complexity of the uncertainty analysis, which typically has many correlated components between the transfer cell and the national reference that partially cancel when the difference is taken. The Measurement Standards Laboratory of New Zealand (MSL) carried out its analysis using a detailed measurement model that included all known correlations and applied an algorithmic approach fully compliant with the Guide to the Expression of Uncertainty in Measurement. As a consequence, MSL submitted an uncertainty value less than half the uncertainty values submitted by almost all of the other participants. This paper describes the measurement model implemented by MSL and demonstrates how accounting correctly for correlations leads to a significantly lower uncertainty. The paper also shows how applying the same method to the previously published NRC analysis results in a reduction in the NRC uncertainty by a factor of about 2.5, making it smaller than the MSL uncertainty.

Abstract The virial coefficients of cryogenic gases, especially helium-4 and helium-3, are playing an ever more critical role in the establishment of primary reference standards for temperature after the redefinition of the kelvin in the SI. Thus, the reliability of the values and uncertainties of these coefficients, especially those of the second, third, and even fourth density virial coefficients ( B, C and D ), has become more significant. To check the accuracy of these coefficients for helium-4 from ab initio calculations, the refractive-index gas thermometry (RIGT) method was developed, allowing for the simultaneous determination of thermodynamic temperatures and density virial coefficients. Using this technique, highly accurate experimental values of B, C and D for helium-4, as well as T – T 90 values, were obtained for the range 5 K–25 K. Direct comparisons with the ab initio calculation density virial coefficients for helium-4 were conducted, revealing excellent agreement. Furthermore, good agreements of thermodynamic temperatures T between absolute RIGT and our previous single pressure RIGT (Gao et al 2021 Metrologia 58 059501) were achieved at temperatures from 5 K to 25 K, with differences within each standard uncertainty. This further strengthens our confidence in the comparisons made in this work. It is foreseeable that the rigorously verified ab initio calculations of the density virial coefficients for helium-4 will continue to be used to improve the measurement accuracy of helium-based primary reference standards for temperature and pressure.

Abstract Probe current stability in a scanning electron microscopy is a critical factor related to the realization of high-precision imaging and accurate nanoscale metrology, including critical dimension measurements and depth estimations. While prior research has predominantly focused on noise sources and long-term drift, systematic quantifications of sensitivity coefficients and measurement uncertainties across various electron gun configurations remain insufficient. Without a clear understanding of how structural parameters such as the tip radius and extractor gap affect probe current stability, optimizing electron sources for advanced metrology continues to be a challenge. Moreover, the lack of experimental validation hinders reliable uncertainty analyses. In this study, we evaluate both short-term and long-term probe current stability levels for thermal field emission and cold field emission sources using Allan deviation and autocorrelation function analyses. Sensitivity coefficients with respect to the extraction voltage are systematically simulated over a range of tip radius and extractor gap distances, revealing direct correlations between geometric design parameters and current stability levels. Experimental measurements are combined with simulation results to quantify the combined standard uncertainty and expanded uncertainty of the probe current for various electron gun configurations. These results establish a clear correlation between emission structure parameters and probe current variations, providing a practical basis for the optimization of electron-optical systems in SEM applications for improved stability and metrology performance outcomes.

Abstract The elementary amount (the amount of substance consisting of a single elementary entity) depends on the unit mole. So, the claim that elementary amount is the defining constant of the mole is circular reasoning. The exact number of elementary entities that define the unit mole is called the Avogadro number. The Avogadro number applies only to the elementary entities referred to in the definition of the mole.

Abstract In the referenced letter to the editor, the authors claim that, because of seemingly circular reasoning by the International System of Units (SI), the Avogadro constant does not have an intrinsic magnitude independent of the mole and therefore cannot be its defining constant. The SI definition of the mole is an aggregate of an exactly specified number of elementary entities. A sample consisting of one elementary entity, the smallest possible amount of any substance, is an elementary amount, dimension N, independent of any chosen macroscopic unit, and equal to the reciprocal of the Avogadro constant. The Avogadro constant itself is then fundamentally equal to one per elementary amount, a physical quantity value with dimension 1/N, independent of the mole, and appropriately recognized as the single defining constant of the current mole definition.